X-ray imaging technology has been employed in a wide range of applications from medical imaging to detection of unauthorized objects or materials in baggage, cargo or other containers generally opaque to the human eye. X-ray imaging typically includes passing high-energy radiation (i.e., X-rays) through an object to be imaged. X-rays from a source passing through the object interact with the internal structures of the object and are altered according to various characteristics of the material (e.g., transmission, scattering and diffraction characteristics, etc.). By measuring changes (e.g., attenuation) in the X-ray radiation that exits the object, information related to material through which the radiation passed may be obtained to form an image of the object.
In order to measure X-ray radiation penetrating an object to be imaged, an array of detectors responsive to X-ray radiation typically is arranged on one side of the object opposite a radiation source. The magnitude of the radiation, measured by any detector in the array, represents the density of material along a ray from the X-ray source to the X-ray detector. Measurements for multiple such rays passing through generally parallel planes through the object can be grouped into a projection image. Each such measurement represents a data point, or “pixel,” in the projection image.
Projection imaging is well suited for finding objects that have material properties or other characteristics such that they produce a group of pixels having a recognizable outline regardless of the orientation of the object to be imaged. However, projection images are not well suited for reliably detecting or characterizing objects that have at least one relatively thin dimension, particularly if these objects may be packaged with other objects, as often occurs in security inspection scenarios. If the rays of radiation pass through only a thin portion of the object or pass through multiple objects, there may be no group of pixels in the projection image that has characteristics significantly different from other pixels in the image. The object may not be well characterized by, or even be detected in, the resultant projection image.
Measuring attenuation of X-rays passing through an object from multiple different directions can provide more accurate detection of relatively thin objects. For instance, in a CT scanner, such measurements may be obtained by placing the X-ray source and detectors on a rotating gantry. An object to be imaged passes through an opening in the center of the gantry. As the gantry rotates around the object, measurements are made on rays of radiation passing through the object from many different directions.
Multiple projection images can be used to construct a three-dimensional, or volumetric, image of the object. A volumetric image is organized in three-dimensional sub-blocks called “voxels”—analogous to pixels in a two-dimensional image—with each voxel corresponding to a density (or other material property) value of the object at a location in three-dimensional space. Even relatively thin objects may form a recognizable group of voxels in such a volumetric image.
The process of using multiple radiation measurements from different angles through an object to compute a volumetric image of the object is herein referred to as volumetric image reconstruction. The quality of volumetric image reconstruction not only depends on the geometry of the imaged object, but also on the geometry of the imaging system including the relative positions of X-ray sources and detectors used to make the measurements. The relative positions of sources and detectors control the set of angles from which each voxel is irradiated by X-rays.
Conventional approaches to volumetric image reconstruction fall into one of two classes: direct reconstruction methods based on formal mathematical solutions to the problem, and iterative reconstruction methods, which calculate the final image in a sequence of small steps. Examples of direct reconstruction methods include filtered back projection and Fourier reconstruction, while examples of iterative reconstruction methods include the Algebraic Reconstruction Technique (ART) and the Simultaneous Iterative Reconstruction Technique (SIRT).